1. Cauchy problems in weighted Lebesgue spaces
- Creator:
- Cholewa, Jan W. and Dlotko, Tomasz
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Cauchy problem, parabolic equation, global existence, and asymptotic behavior of solutions
- Language:
- English
- Description:
- Global solvability and asymptotics of semilinear parabolic Cauchy problems in $\mathbb R^n$ are considered. Following the approach of A. Mielke [15] these problems are investigated in weighted Sobolev spaces. The paper provides also a theory of second order elliptic operators in such spaces considered over $\mathbb R^n$, $n\in \mathbb N$. In particular, the generation of analytic semigroups and the embeddings for the domains of fractional powers of elliptic operators are discussed.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public